It depends on what you mean by time travel. Usually people mean closed timelike curves exist, and this won't happen in your example. If there are no closed timelike curves in S, there will be no closed timelike curves in S'.

According to Matt Visser, a Roman ring is a configuration of *several* wormholes such that the whole configuration is a time machine, but such that no pair of mouths for a single wormhole is a time machine.

As in your example, in all frames, there is a spacelike identification between mouths of each individual wormhole, so each individual wormhole is not a time machine. In order for a single wormhole to be a time machine, the identification between mouths has to be timelike. See the second link I give in post #3 of this thread.

Yes, it's possible two create a time machine with two wormholes that all have mouths moving inertially, but in your previous two posts you said explicitly that it could be done with only one wormhole that had mouths moving inertially.

You are correct, only the configuration consisting of two wormholes having uniform relative motion with each other and sufficiently close, can form a time machine. This example clearly shows how much problematic is the idea of wormholes with relationship to causality.

In the past 4. was often assumed, but since global hyperbolicity is a very strong global condition and Einstein's equations are (local) differential equations, many physicists have moved to 2. and 3. Stephen Hawking likes 3., for example, and has formulated the Chronology Protection Conjecture, "It seems that there is a Chronology Protection Agency wich prevents the appearance of closed timelike curves and so makes the universe safe for historians."

This roughly states that near a chronology horizon (horizon at which spacetime becomes causally ill-behaved), expectation values of stress-energy tensors for quantum fields blow up, thus preventing (by wall-of-fire barriers) physical objects from crossing chronology horizons. There seems to be some semi-classical evidence for this conjecture, but a more refined analysis by Kay, Radzikowski, and Wald muddies the picture a bit. Their analysis shows that the semi-classical stress-energy tensor is ill-defined, but not necessarily infinite, at a chronology horizon.

This may be just an indication that the semi-classical theory breaks down at chronology horizons, and that full quantum gravity is needed for definitive predictions.

In the interface region between quantum field theory and general relativity I (ed: Visser, not me!) have been heavily involved in trying to get a deeper understanding of the energy conditions and the extent to which they should be trusted. (Not only do one-loop quantum effects violate all the energy conditions, but even certain quite seemingly sensible looking classical systems violate all the energy conditions.) The implications are potentially disturbing.

The usual example of the problem of believing that the energy conditions always hold is the Casimir effect. Other examples include the space-time outside but near the event horizon of a black hole. If it didn't have negative energy density, hawking radiation would be impossible. We don't have any experimental confirmation of Hawking radiation, of course, but we do have experimental confirmation of the Casimir force.

According to Barcelo and Visser's Twilight for the energy conditions?, the trace energy condition is forgotten, the null, weak, and dominant energy conditions are all moribund, and the strong energy condition is dead.

I believe (3) may hold in the end. i.e. A correct theory of Quantum Gravity may prevent a wormhole to become traversable in the first place. If there is no travel possible through wormhole, no space like intervals appear in any frame of reference thus effectively excluding the possibility of closed time like curves.

As far as I know, any traversable wormhole violates at least one of the energy conditions.

pervect said:

It appears to be difficult to do this, though.

Ok, I'm not able to contribute much. I have read that negative energy in all known forms seems to be unable to produce time travel possibilities. My guess is that this will hold in a TOE, too. Some cool equation will appear there to prove it.